A new approach has been taken to the protein folding problem. It is a general approach that yields all possible topologies of the protein chain, but not yet all of its atomic details. It affords an enormous reduction in the number of protein conformations that it is necessary to consider for the complete problem. The procedure is to generate all possible compact conformations, and to assess their quality in a general way, based upon what has been observed in globular protein crystal structures. This effectively leads to "fuzzy" protein conformations, with only the major features of the residues that are close to one another. We have generated, on cubic lattices, all possible conformations of crambin and trypsin inhibitor. In each case only several thousand conformations are possible in their limited space. For example for crambin this represents a reduction from around 10**30 to about 2000 conformations. To assess the merits of these conformations, we use effective residue-residue interaction energies statistically derived from protein X-ray structures. The native conformations have been observed always to fall in the best 1 to 10% of the conformations, yielding a further reduction of at least an order of magnitude in the number of conformations that must be subsequently considered. We plan to develop procedures to include all atoms and refine with conventional energy calculations, for the best few hundred of these conformations.